## Algebra 2 Common Core

$$\sin^{2}\theta$$
Simplify $$\sec\theta\cos\theta-\cos^{2}\theta.$$ Use the Reciprocal Identity $$\sec\theta=\frac{1}{\cos\theta}$$ to obtain $$\sec\theta\cos\theta-\cos^{2}\theta=\bigg(\frac{1}{\cos\theta}\bigg)\cos\theta-\cos^{2}\theta=1-\cos^{2}\theta.$$ The Pythagorean Identity states $$\sin^{2}\theta+\cos^{2}\theta=1$$ or $$1-\cos^{2}\theta=\sin^{2}\theta.$$ So $$\sec\theta\cos\theta-\cos^{2}\theta=\sin^{2}\theta.$$